A blog is that is all about mathematics and calculators, two of my passions in life.

Tuesday, March 17, 2015

Quilts: Finding the Number of Blocks That Fit in a Rectangle

Quilts: Finding the Number of Blocks That Fit in a
Rectangle

The program
QUILT will find the number of small tiles that will fit in a large rectangular
quilt (this can be applied to game boards, posters, or other decorative
items). QUILT will also calculate the
number of columns and rows of tiles you will have, and the leftover area. The idea is to minimize the area that remains
after placing the maximum amount of tiles.
I will assume that no tiles will be cut in the process.

Fitting Tiles to a Quilt

Where:

bw = width of
the quilt (labeled A on the Prizm program QUILT)

bl = length of
the quilt (labeled B on the Prizm program QUILT)

sw = width of
the tile (labeled C on the Prizm program QUILT)

sl = length of
the tile (labeled D on the Prizm program QUILT)

Formulas

Number of tiles
that can fit:

n = floor(bw/sw)
* floor(bl/sl) = int(bw/sw) * int(bl/sl)

where floor is
the floor function and int represents the integer function. Essentially, you want the integer (whole
number) portion of the divisions sw/sl and bw/bl and disregard the fraction
part.

Number of
columns of tiles = floor(bw/bl)

Number of rows
of tiles = floor(sw/sl)

Leftover area =
bw * bl – n * sw * sl

Thanks to

Casio Prizm: QUILT

“QUILT WIDTH AND”

“LENGTH:”

? -> A

? -> B

“TILE WIDTH AND”

“LENGTH:”

? -> C

? -> D

Int (A÷C) * Int
(B÷D) -> N

AB – NCD -> L

“NUMBER OF TILES”

N ◢

“COLUMNS=”

Int (A÷C)◢

“ROWS=”

Int (B÷D)◢

“AREA LEFTOVER=”

L

HP
Prime: quilt

quilt()

BEGIN

LOCAL bw, bl, sw, sl, n, l;

INPUT({bw,bl},”Quilt”,{“Width:”, “Length:”});

INPUT({sw,sl},”Tile”,{“Width:”, “Length:”});

n:=FLOOR(bw/sw)*FLOOR(bl/sw);

l:=bw*bl-sw*sl*n;

PRINT()
PRINT(“# of tiles = “+ n);

PRINT(“# of columns = “+FLOOR(bw/sw));

PRINT(“# of rows = “+FLOOR(bl/sl));

PRINT(“Leftover Area = “+l);

RETURN {n,FLOOR(bw/sw),FLOOR(bl/sl),l};

END;

Examples

Example 1:

We have a quilt that measures 40” by 54” and we want to fit as many
tiles measuring 2” by 3”. Hence: bw = 40, bl = 54, sw = 2, and sl = 3.

Result:

Number of tiles: 360

Number of columns: 20

Number of rows: 18

Leftover area: 0 (perfect fit!)

Example 2:

We have a quilt that measures 48” by 54” and we want to fit as many
tiles measuring 5” by 5”. Hence: bw = 48, bl = 54, sw = 5, and sl = 5.